lightpointe historical free space optics info physics of free-space optics
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802-0006-000 2 May 2002 1
THEPHYSICSOFFREE-SPACEOPTICS
Scott Bloom, PhDChief Technical Officer
AirFiber, Inc.
INTRODUCTION
Several key factors are bringing free-space optical technology (FSOT) into the
carrier space as a means of broadband access. The first is a growing and seem-
ingly insatiable bandwidth demand in the marketplace. FSOT technology pro-
vides fiber-optic like speeds without significant initial capital expenditures forscarce resources such as spectrum. Deregulation of the telecommunication
industry in the US and abroad has introduced a new class of carriers that pro-
vide broadband services and require scaleable and affordable infrastructure
equipment to bring those services to their customers. While fiber-optic rings are
becoming ubiquitous, providing the bandwidth from these rings to customers
remains challenging. While FSOT infrastructure sounds inviting, there are
many near-term hurdles for FSOT products. Availability is the primary cus-
tomer concern for FSOT products. Proof of availability needs to be statistically
demonstrated with real FSOT systems in the field before there is widespread
customer acceptance of the technology. Other concerns are compatibility with
existing LEC networks and premise networks, cost, carrier-class hardware, ease
of installation, and network management.
This documents primary purpose is to explain and clarifyusing real data col-
lected by AirFiber and othersthe system design issues of free-space optical
technologies. The physics of the atmosphere dictate some very specific perfor-
mance limitations on free-space systems that can be derived very generally to
put an upper bound on carrier-grade range expectations and claims by many
vendors in the industry. As a secondary purpose, this paper discusses features
associated with a free-space optical system that can be considered performance
enhancing. These are aspects of free-space systems that provide added function-
ality to users, perhaps expanding the market for which free-space technology
can be applied. Finally, this paper summarizes the system design discussions
into some simple design rules for carrier-class free-space optical systems.
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The Physics of Free-Space Optics 2
This document is organized as follows:
Free Space Optics System Design Issues
Subsystems
Discussions of the various major subsystems that constitute a free-space optical
system. Each of the subsystems is discussed in terms of example point designs in
the marketplace.
Link EquationsHigh-level discussion of the main factors in the system link equation. Addition-
ally, the relative importance of each of these factors is compared in realistic
weather conditions
Comparison Link Budgets
Link budgets for point designs that are offered in the marketplace. Most of the
data for these designs is available via the vendor's data sheets or from the world
wide web. If an assumption is made about a component, that fact is noted.
Availability
Actual weather statistics from nephelometers and AirFiber free-space optical
communications systems are used to compute link range as a function of avail-
ability for carrier-class numbers (99.9% or better).
Theoretical Maximum Range
A straw-man design is used to compute the maximum range in 200 dB/km atten-
uation conditions. Since this is not obtainable, it sets an upper limit on range for
free-space systems. The maximum range as a function of availability is also pre-
sented for several cities.
Bit Error Rate, Data Rate, and Range
Theoretical curves of BER and data rate show that reducing data rate or relaxing
BER constraints does not significantly increase the maximum range in realistic
weather scenarios.
1550 nm versus 785 nm
The debate over propagation characteristics of near infrared (IR) versus 1550 nm
light is resolved by curves generated by multiple scattering codes from visiblethrough millimeter waves.
Free Space Optics Systems Enhancements
Tracking
The requirements for tracking systems in carrier-class free-space optics systems.
Physics of Scintillation
Scintillation effects and techniques for mitigating the detrimental effects of scin-
tillation.
Power Control and Eyesafety
The benefits of power control for long-term laser reliability and eyesafety
Design Philosophy and Design Rules for Carrier-Grade Free-Space OpticsSystems
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The Physics of Free-Space Optics 3
FREE-SPACEOPTICSSYSTEMDESIGNISSUES
Free-Space Optics Subsystems
Figure 1 illustrates the major subsystems in a complete carrier-grade free-space optics
communications system. The optical apertures on a free-space system can have an
almost infinite variety of forms and some variety of function. They can be refractive,
reflective, diffractive, or combinations of these. In figure 1, the transmit, receive, and
tracking telescopes are illustrated as separate optical apertures; there are several other
configurations possible where, for example, a single optic performs all three functions
thereby saving cost, weight, and size. On the transmit side, the important aspects ofthe optical system are size and quality of the system. Size determines the maximum
eye-safe laser flux permitted out of the aperture and may also prevent blockages due to
birds. Quality, along with the f-number and wavelength, determine the minimum
divergence obtainable with the system. On the receive side, the most important aspects
are the aperture size and the f-number. The aperture size determines the amount of
light collected on the receiver and the f-number determines the detector's field of view.
The tracking system optics field of view must be wide enough to acquire and maintain
link integrity for a given detector and tracking control system.
Figure 1. Free-Space Optics Major Subsystems
Transmit OpticLaserDriver
Receive OpticDetectorPreamp
Tracking OpticSpatial
DetectorPreamp
Az/El servo system
Az/El control system
Main Micro-
processor
Demodulator
ModulatorData In
Data Out
Thermal
Humidity
De-icing
Control
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The Physics of Free-Space Optics 4
Several means are available for coupling the laser to the output aperture. If a discrete
diode is used, the diode is usually micro-lensed to clean up the astigmatism of the out-
put beam and then is free-space coupled to the output aperture by placing the laser at
the focus of the output aperture optical system. The coupling system is very similar for
fiber lasers because the core of the fiber laser and the output aperture of a Fabry-Perot
laser have similar sizes. The distance from the laser aperture to the output aperture
must be maintained such that the system divergence remains in specification over the
temperature ranges encountered in an outdoor rooftop environment. This can beaccomplished with special materials and/or thermal control.
Diode lasers are driven with a DC bias current to put the devices above threshold, and
then, on top of that, are modulated with an AC current to provide, for example, on/off
keying (OOK) for data transmission. For lasers with output powers below approxi-
mately 50 mW, off-the-shelf current bias and drive chips are available; for higher power
lasers, custom circuits or RF amplifiers are generally used.
The receive detector is coupled to the receive aperture through either free-space or
fiber. Depending on the data rate and optical design alignment, tolerances can be
extremely restrictive. For example, for data rates to 1.25 Gbit/s, detectors with rela-
tively large active areas (500-micron diameter) can be used, making alignment to the
receive aperture fairly straightforward. For fiber-optic coupling into multimode fibers,the correct size is about 63 microns in diameter, which makes alignment much tougher.
The use of special materials or controls is required in this case, however, coupling is
more modular.
Detectors are generally either PIN diodes or avalanche photodiodes (APD). For carrier-
class free-space optics systems, an APD is always advantageous since atmospheric-
induced losses can reduce received signals to very low levels where electronics noise
dominates the signal-to-noise (SNR) ratio. Of course the APD must be capable of meet-
ing the system bandwidth requirements. Usually a trans-impedance amplifier is used
after the detector because in most cases they provide the highest gain at the fastest
speed.
If CCD, CMOS, or quad cell detectors are used as tracking detectors, these relativelylarge area devices are easy to align to the tracking optics. However, care must be taken
in manufacture to co-align these optics with the transmit and receive optical axes. For
building-mounted free-space optical systems, the tracking bandwidth can be very low
sub-hertzbecause the bulk of building motion is due to the buildings uneven thermal
loading and these effects occur on a time scale of hours. For systems that are to be
mounted on towers or tall poles, the tracking bandwidth should be highermost likely
on the order of several hertz at leastto remove wind-induced vibrations.
Acquisition systems can be as crude as aligning a gunsight to very sophisticated GPS-
based, high accuracy, fully automated systems. The choice of this subsystem really
depends on the application and number of devices to be put into a network.
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The Physics of Free-Space Optics 5
The Free-Space Optic Link Equation
The link equation for a free-space optical system is actually very simple at a high level
(leaving out optical efficiencies, detector noises, etc.). The equation is illustrated in fig-
ure 2. The amount of received power is proportional to the amount of power transmit-
ted and the area of the collection aperture. It is inversely proportional to the square of
the beam divergence and the square of link range. It is also inversely proportional to
the exponential of the product of the atmospheric attenuation coefficient (in units of 1/
distance) times the link range.
Figure 2. Basic FSO Link Equation
Looking at this equation, the variables that can be controlled are: transmit power,
receive aperture size, beam divergence, and link range. The atmospheric attenuation
coefficient is uncontrollable in an outdoor environment and is roughly independent of
wavelength in heavy attenuation conditions. Unfortunately, the received power is expo-
nentially dependent on the product of the atmospheric attenuation coefficient and the
range; in real atmospheric situations, for carrier-class products (i.e., availabilities at99.9% or better) this term overwhelms everything else in the equation. This means
that a system designer can choose to use huge transmit laser powers, design large aper-
tures, and employ very tight beam divergences, but the amount of received power will
remain essentially unchanged. Figure 3 illustrates this point. Except for clear air, the
atmospheric loss component of the link equation dominates by many orders of magni-
tude, essentially obviating any system design choices that could affect availability.
Designers of free-space systems that are to be carrier class must accept this fact and
design the system accordingly. Basically, the only other variable under the designer's
control is link range, which must be short enough to ensure that atmospheric attenua-
tion is not the dominant term in the link equation. As discussed in a later section, this
implies the link range mustbe less than 500 m. However, efficient designs can be pro-
duced that permit economical, reliable operation under this constraint.
)exp (
A
2
receiverRange
RangeDivPtransmitPreceived
Receiver area
Beam
divergence
Atmospheric
Attenuation Factor
.=)(. .
.
)( 1km
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The Physics of Free-Space Optics 6
Figure 3. Geometric and Atmospheric Loss Components
Comparison Link Budgets
Figure 4 shows a tabular link budget for the top five free-space optical system manufac-
turers. Most of the system parameters are freely available from manufacturers data
sheets; where a parameter has been assumed it is noted. One of the vendors (high-lighted) has a product at 155 Mbit/s and really should not be compared with the others
at 1.25 Gbit/s but has been included for informational purposes. The atmospheric
attenuation condition is 200 dB/km. The link ranges were adjusted for each system
such that the margin came out to approximately zero. It is interesting to note the wide
variety of adjustable system parameters (aperture size, wavelengths, transmit diver-
gences, transmit powers) that have been employed in these systems yet, as previously
discussed, the maximum link ranges are all about the same (approximately +/ 30 m).
This again illustrates the point that system designers do not have a lot of options avail-
able to increase link range in realistic carrier-grade atmospheric conditions. Given that
all manufacturers have about the same performance in high attenuation conditions,
figure 5 plots the maximum range versus atmospheric attenuation (dB/km) for one of
the vendors, which is about the same for all of the vendors. It is interesting to note that
at longer ranges (about 1 km or so) the maximum attenuation allowable is about 3040
dB/km. It turns out that heavy rain can produce this range of attenuation values and
therefore the long link range issue is going to be widespread throughout the world, and
not just limited to foggy coastal areas.
0 100 200 300 400 500 600 700 800 900 10001 10 201
10 19110 18110
171 10 161
10 15110 14110 13110 12110 11110 10110 9110 8110 7110 6110 5110 4110 30.01
0.1
1
10
100
1 10311041105
1 1030 R
MultiplicativeFactor
Geometric
losses
receiver
(Div Range )
A2
8.6 dB/km2000 m visibility exp(- Range)2
km
130 dB/km130 m visibility
)exp(- Range30km
200 dB/km
85 m visibility
exp(- Range)46km
1.053 10 20
2.25 104
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The Physics of Free-Space Optics 7
Figure 4. FSO Performance Comparison (I)
Figure 5. FSO Performance Comparison (II)
AirFiber Vendor A Vendor B Vendor C Vendor D
AtmosLoss
dB/km -200 -200 -200 -200 -200
Transmitter AlGaAs
Modulation Format NRZ OOK
Receiver Si APD
Wavelength 785 850 1550 1550 850 nm
Range 200 190 215 205 176m
Data Rate 1250 1250 1250 155 1250 Mbit/s
Average Laser Power 18 30 1000 320 15.6 mW
Peak Laser Power 36 60 2000 640 31mW
Transmit Aperture 5 5 16 2.5 5 cm
Transmit Divergence 0.5 2 2 4.25 2mrad(1/e^2)
Receive Aperture 7.5 20 40 20 19cm
Optical Background 0.2 0.2 0.2 0.2 0.2 W/m 2/nm/sr
Receiver FOV 3.25 3.25 3.25 3.25 3.25 mrad(1/e 2)
Receive Filter Width 25 25 25 25 25 nm
Receiver Sensitivity 800 1000 1000 1000 1000nW
BER 1.00E-12 1.00E-12 1.00E-12 1.00E-12 1.00E-12
Peak Laser Transmit Power -14.43697499 -12.2184875 3.010299957 -1.93820026 -15.08638306 dBW
Extinction Ratio Degradation -0.2 -0.2 -0.2 -0.2 -0.2 dB
Transmit Optics Degradation 0 0 -15 0 0 dBW
Pointing Loss -1 -1 -1 -1 -1 dB
Geometric Range Loss -2.498774732 -5.575072019 -0.628169285 -12.78225591 -5.355781251 dBAtmospheric Loss -40 -38 -43 -41 -35.2 dB
Atmospheric Sc intillation Fade -1 -1 -1 -1 -1 dB
Receive Optics Attenuation -1.4 -1.4 -1.4 -1.4 -1.4 dB
Bandpass Filter Loss -0.7 -0.7 -0.7 -0.7 -0.7 dB
Misc Loss Elements 0 0 0 0 0 dB
Received Peak Power at Detector -61.23574972 -60.09355952 -59.91786933 -60.02045617 -59.94216431 dBW
Required Peak Power at Detector -60.96910013 -60 -60 -60 -60 dBW
Link Margin at Range -0.266649594 -0.093559515 0.082130672 -0.020456169 0.057835688 dB
Attenuation(dB/km)
Range (m)
Theoretical preliminary link budget at 1.25 Gbit/s, 10 BER-12
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The Physics of Free-Space Optics 8
Availability
A carriers key issue in deploying free-space optical systems is system availability. Sys-
tem availability comprises many factors, including equipment reliability and network
design (redundancy, for example) but these are well known and fairly quantifiable. The
biggest unknown is the statistics of atmospheric attenuation. While almost all major
airports around the world keep visibility statistics (which can be converted to attenua-
tion coefficients), the spatial scale of visibility measurements is rough (generally 100 mor so) and the temporal scale is infrequent (hourly in most cases). With the crude spa-
tial and temporal scales, estimates of availability for carrier-grade equipment (99.9% or
better) are going to be limited to 99.9% or worse. Therefore, these huge databases are
not useful except for estimating the lowest acceptable carrier grade of service. Better
data is needed to permit carriers to write reasonable service level agreements. AirFi-
ber has had instruments capable of acquiring this data running continuously for
approximately two years. These instruments, which include a nephelometer and an in-
house designed and built weather benchmark system, allow the collection of data at the
correct spatial and temporal resolution for accurate estimates of availability versus
link range.
Figure 6 shows a plot of this data for two cities, Tokyo and San Diego. One line shows
the cumulative probability density function for San Diego and the other shows thesame information for Tokyo. Also plotted is the link budget equation for an AirFiber
product; other vendors products have about the same link margins. The left vertical
axis shows the percentage of time that the attenuation is greater than or equal to a
given value. The horizontal axis is attenuation in dB/km, and the vertical axis on the
right side is the maximum link range at zero link margin. To use the chart, choose an
availability, say 99.9% (as shown by the dotted line), move horizontally to the desired
city (say Tokyo in this example), move vertically to the link budget equation, and
finally move horizontally to the maximum link range (in the case of Tokyo, about
350 m). It is interesting to note that Tokyo is qualitatively in the top 10% of cities for
clarity of the atmosphere and San Diego is in the bottom 10%. Therefore for most
deployments, the maximum range will fall somewhere in between these two cities, cer-
tainly less than 500 m in most cases.
Figure 6. FSO Availability
Tokyo and San Diego Availability (1999-2001)
0.0001
0.001
0.01
0.1
1
10
100
0 50 100 150 200 250 300 350
dB/km
1-Availability(%)
0
100
200
300
400
500
600
700
800
900
1000
Range(m)
1-Availability:Tokyo
Range
1-Availability: San Diego
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The Physics of Free-Space Optics 9
Theoretical Maximum Range
As a final statement about the performance of free-space optical systems in realistic
weather conditions, we perform calculations of maximum link ranges for a strawman
theoretically "perfect"but as yet unobtainablefree-space optical system. Figure 7
illustrates the assumptions and results of this calculation. Under the assumptions it is
worthy to note that the detector, electronics, and background noise were set to zero and
the collection aperture was assumed to receive alltransmitted photons; that is, beamdivergence was set at zero. In addition, a very large transmit aperture was chosen so
that 80 watts of transmit power could be used and still maintain eye-safe levels. Run-
ning through the numbers for 200 dB/km and 10-12BER at 1 Gbit/s data rate results in
a maximum range of about 500 m. So even in an "unobtainable" system, the maximum
range in realistic atmospheric attenuation situations is about 500 m.
Figure 7. Strawman Perfect FSO Link
Figure 8 further illustrates this point and correlates this system with real availability
data for several cities around the world. In this figure the 99% line can be as high as
several kilometers in some cities as illustrated by the 99% rectangle. As soon as carrier-
grade availability of 99.9% is used, the box shrinks significantly as illustrated by the
99.9% rectangle in the figure. The maximum range in this carrier-grade case is about
900 m; if Chicago is taken out of the data set, the maximum range is 600 m.
Assumptions
Eye-safe laser
No detector/electronics
or background noise
No geometrical loss
25.4 cm aperture
80 W transmit power
200 dB/km Attenuation
Need SNR=14 for 10 BER-12
No geometrical loss
Results
Bh
P
SNR
signal
= 2
1
nWWRange
9.81080 10200
=
Range = 497 meters
1 Gbit/s
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The Physics of Free-Space Optics 10
Figure 8. Theoretical Link with 63 dB Margin
Bit Error Rate, Data Rates, and Range
In figure 9, which depicts a set of buildings in Denver, Colorado, we illustrate the
effects of fog on visibility range. The tall building in the foreground is about 300 m
from the photographer. The left photo shows clear air, at 6.5 dB/km (2000 m visibility
range), as measured with a nephelometer mounted at the photographer's site. Note
that the distant mountain ranges are easily visible at many miles distance. During a
fog which measured about 150 dB/km (visibility range of about 113 m), as shown in the
middle photo, the building is still visible at 300 m, but the scenery is washed out
beyond this range. As shown in the right photo, at 225 dB/km (visibility range of about
75 m) the building is completely obscured.
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The Physics of Free-Space Optics 11
Figure 9. Denver, Colorado Fog/Snowstorm Conditions
For free-space optical systems, the questions of bit error rate (BER) versus range and
data rate versus range frequently arise. Unlike fiber-optic systems where the channel
is well known and characterized, free-space systems have severe atmospheric attenua-
tion propagation conditions that cause the BER to behave in an almost binary manner.
This is illustrated in figure 10, showing the BER versus range for a Gigabit Ethernet
system in 200 dB/km attenuation conditions. The graph clearly illustrates that relaxing
the BER requirement from, for example, 10-12 to 10-6results in a range gain of only
1015 m. Because free-space systems in general, under carrier-grade conditions, are
either error free or fully errored when severe atmospheric attenuation is encountered,
it does not make sense to design for moderate bit error rates. The same is true for data
rate as shown in figure 11, where the data rate for the same system was reduced to 100
Mbit/s. In this case, the gain in range is only 30 m at 10-12BER. In carrier-grade condi-tions, the best design for free-space optical systems is to push the components to their
limits in terms of speed and BER performance, reducing these factors does not buy a
significant increase in range performance.
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The Physics of Free-Space Optics 12
Figure 10. BER versus Range at 1.25 Gbit/s
1550 nm Versus 785 nm
Another topic frequently discussed concerning the performance of free-space optical
systems is the issue of atmospheric propagation and wavelength. One generally held
belief is that a system operating at longer wavelengths has better range performance
than systems at shorter wavelengths. Figure 12 shows several calculations performed
using MODTRAN for a 1 km path length for which the x-axis is wavelength. The visi-
bility range was 200 m, typical of an advection fog. The y-axis in the top panel is trans-
mission from a minimum of 0 to a maximum of 1. The top panel shows the amount of
absorption due to water only in the atmosphere. Here many wavelengths propagate
very poorly due to absorption by water vapor, particularly near 1.31.4 microns. The
second panel from the top shows absorption due to oxygen and carbon dioxide, which
are relatively narrow lines and are easily avoided.
The third panel shows the effects of Mie scattering by water droplets in the fog. Clearly
this is the dominant loss mechanism under these conditions and is basically indepen-
dent of wavelength (for example, it is actually a little worseat 1.5 microns than at
785 nm). Finally, the bottom panel shows the combined effects of all three loss mecha-
nisms. Again the result is basically independent of wavelength. There is no advantage
in propagation range by using longer wavelengths. Taking this one step further, the
calculations were performed at even longer wavelengths as illustrated in figure 13.
Here the x-axis is again wavelength, the y-axis is the combined loss over a 1 km path.
In these illustrations the vertical axis is attenuation in dB/km. For all wavelengths up
to about 12 microns the result is the same. There are no "spectral holes" in which it is
very advantageous to propagate; the attenuation is basically flat over these wave-
lengths. Finally the same calculations were carried out all the way to millimeter waves,
as illustrated in figure 14. This was done for completeness and to make sure that at RF
frequencies the attenuation reduced to generally accepted values. Not until the wave-
length is at sub-millimeter size (RF) is attenuation markedly reduced.
165 170 175 180 185 190 1951.10
151.10
141.10
131.10
121.10
111.10
101.10
91.10
81.
10
71.10
61.10
51.10
41.10
30.01
0.10.041
2.3 10 15
.
P e Range V t Range( ),
195165 Range
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The Physics of Free-Space Optics 13
Figure 11. BER and Range versus Data Rate
184 186 188 190 192 194 1961.10221.
10211
.10201
.10191
.10181
.10171
.10161
.10151
.10141
.10131
.10121
.10111
.10101
.1091
.108
1.859 109
.
2.984 1022.
P e Range V t Range( ),
195185 Range
160 170 180 190 2001.10
151.10
141.10
131.10
121.10
111.10
101.109
1.1081
.1071
.1061
.1051
.1041
.1030.010.1
0.041
2.3 1015
.
P e Range V t Range( ),
195165 Range
Decreasing the data rate from 1.25 Gbit/s to 100 Mbit/s
increases the range for 10 BER by only about 30 meters
in 200 dB/km attentuation
-12
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The Physics of Free-Space Optics 14
Figure 12. 1550 nm versus 780 nm Atmospheric Propagation
Figure 13. Wavelength versus AttenuationNear Infrared
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The Physics of Free-Space Optics 15
Figure 14. Wavelength versus Attentuationthrough Millimeter Waves
In summary we can clearly state that for the majority of cities around the world, the
carrier-class distance (as defined by 99.9% availability or better) is less than 500 m. In
addition, despite numerous claims, all free-space optics vendors have about the same
range performance in carrier-grade conditions (99.9% or better) due to complete domi-
nation of the link budget equation by the atmospheric attenuation factor in high atten-
uation situations. Finally, wavelength has absolutely no effect on propagation range
under carrier-grade conditions for wavelengths from visible all the way up to millime-
ter wave (RF) scales.
FREE-SPACEOPTICSSYSTEMSENHANCEMENTS
Tracking
One issue that is debated among free-space optics vendors is the necessity of having a
tracking system. The question is whether the hardware needs to compensate for small
amplitude, low frequency, building motionusually thermally inducedto maintain
link integrity or is it sufficient to spread the divergence of the transmitter beam large
enough to encompass all foreseeable building movement amplitudes? Going back to the
link equation, it is easy to see that spreading the beam divergence impacts the link
margin by the inverse square of the spread. In other words, every doubling of the beam
divergence negatively impacts the link margin by 6 dB. In addition, even if the beam is
spread broadly enough to accommodate building motion, the overall system link mar-
gin will fluctuate negatively and/or degrade since, by design, precise alignment of free-
space optical systems will not always be achieved over time and temperature.
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The Physics of Free-Space Optics 16
Figure 15 illustrates this effect with actual data from a fielded system (distance of
500 m) running live customer traffic in Phoenix, Arizona. The upper graph shows the
change in azimuthal position as a function of time. The x-axis units are arbitrary; how-
ever, the pattern of peaks and valleys is due to diurnal thermal changes at the site. The
same is true of the bottom graph but for the elevation axis. One tick on either vertical
axis corresponds to about 100 microradians of motion, so the maximum azimuthal vari-
ation (building twist) is about 1.5 milliradians, and the maximum elevation variation is
about 2.5 milliradians. In fact we have observed elevation variations of 8 milliradianson this same link under different thermal conditions. Another interesting point to note
is that a competitor's non-tracking units were removed from this link because they con-
sistently lost link during diurnal thermal cycles. To illustrate the importance of track-
ing, loss of link margin due to building motion was calculated for non-tracking units. If
the 1/e2beam divergence is 2 milliradians and the links are perfectly aligned at instal-
lation, a 1 milliradian building motion would incur a loss of link margin of about
8.6 dB. Even if the link stayed up during this excursion, system performance would be
degraded by 8.6 dB from the initially specified margin. This means that for a typical
carrier-grade link of 200 m, in the absence of tracking the system can withstand about
43 dB/km lessatmospheric attenuation than the initial design. For calibration, heavy
rain can induce about 1740 dB/km of attenuation, so a system that is designed to han-
dle heavy rain could be down in a severe storm.
Figure 15. Tracking ExampleCustomer Network in Phoenix, AZ
Elevation Variation
-100
-80
-60
-40
-20
0
1
576
1151
1726
2301
2876
3451
4026
4601
5176
5751
6326
6901
7476
8051
8626
9201
9776
10351
Time
1countis100microrads
Data from customer
running live traffic,
500 m range
AirFiber units replaced
competitor's non-
tracking units
Non-tracking multi-
laser units regularly
lost communications
during diurnal cycle;
maximum 8 mrad
excursion measured
Azimuth Variation
4090
4095
4100
4105
4110
4115
4120
1
589
1177
1765
2353
2941
3529
4117
4705
5293
5881
6469
7057
7645
8233
8821
9409
9997
Time
1countis100microrads
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The Physics of Free-Space Optics 17
Physics of Scintillation
Atmospheric scintillation, as used in this document, can be thought of as changing light
intensities in time and space at the plane of a receiver detecting the signal from a
transmitter at a distance. The received signal level at the detector fluctuates due to
thermally induced changes in the index of refraction of the air along the transmit path.
The index changes cause the atmosphere to act like a collection of small prisms and
lenses that deflect the light beam into and out of the transmit path. The time scale ofthese fluctuations is about the time it takes a volume of air the size of the beam to move
across the path and therefore is related to wind speed. There are many theoretical
papers written on this effect, primarily for ground-to-space applications, and in gen-
eral, are very complicated. It has been observed that for weak fluctuations, the distri-
bution of received intensities is close to a log normal distribution. For the case of free-
space optics, which implies horizontal path propagation and therefore stronger scintil-
lation, the distribution tends to be more exponential.
One parameter that is often used as a measure of the scintillation strength is the atmo-
spheric structure parameter or Cn2. This parameter, which is directly related to wind
speed, roughly measures how turbulent the atmosphere is. Figure 16 illustrates some
measurements of this parameter taken at the AirFiber facility in San Diego, CA. The
most interesting feature of the data is the fact that the parameter changes by over anorder of magnitude over the course of a day, with the worstor most scintillatedmea-
surements occuring during midday when the temperature is the greatest.
Figure 16. Scintillation and Measured Cn2in San Diego, California
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The Physics of Free-Space Optics 18
The variation in Cn2is interesting because Cn2can be used to predict the variance in
intensity fluctuations at the receiver using the formula displayed at the top of
figure 17. The variance is linearly proportional to Cn2, nearly linearly proportional to 1/
wavelength, and nearly proportional to the square of the link distance. Two interesting
facts can be inferred from this. First, shorter wavelength systems have proportionally
larger variance in the scintillation intensity. For example a system operating at 780 nm
has about twice the variance as a system operating at 1550 nm. Second, the effect
increases severely with range. At twice the range, the variance is four times greater.The graphs represent the variance as a function of range for the minimum, median,
and maximum values of Cn2measured in figure 16.
Figure 17. 2from Cn
2
0 500 1000 1500 20001.10
3
0.01
0.1
1
103.955
1.303 10 3
.
2 103
.100 L
C nsq k, L, 0.31 C nsq. k
7
6. L
11
6.
Variance in intensity
fluctuation is derived
from atmospheric
structure constant
Scintillation effects
scale (become worse)
like Range2
2
2
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The Physics of Free-Space Optics 19
The effects of scintillation are graphically illustrated in figure 18. The figure depicts a
receiver aperture with dark and light "speckles" distributed randomly over the aper-
ture. The size of these speckles scales like (R)1/2. Again there are two interesting fea-tures to note about this scaling. First, the longer the wavelength, the larger the
speckle. This is not good for system performance because the smaller the number of
speckles at the receiver aperture, the less aperture-averaging over the various intensi-
ties of each speckle can occur. If the receive aperture is collecting only one speckle, for
example, then a very large increase in system transmit power is required to ensurethat the BER is maintained even for a "dark" speckle. Second, the size scales like the
square root of the link distance; longer links imply larger speckles, which impacts sys-
tem performance as previously described.
Figure 18. Scintillation Spots and Aperture Averaging
Scintillant
1/2
Receive
Aperture
Turbulence in the
atmosphere causes
random shifts in wave-
front phase and intensity
Scintillation patterns of
very bright and very dark
spots are projected on
the receive aperture
(R)
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The Physics of Free-Space Optics 20
Figure 19 shows the effects of aperture averaging on the required link margin for a
3-inch aperture. The plots are for a 100-m link and a 1000-m link. The 100-m link
shows a received intensity distribution that is nearly Gaussian, centered about the
mean transmit intensity of 1. Here, scintillation plays no role; in fact for nearly allcar-
rier-grade links (ranges of less than 500 m) scintillation effects are a few dB at most. At
1 km, the intensity distribution is more skewed and requires about 13 dB more power
for the same BER as the 100-m link (to overcome scintillation, not geometrical effects).
The point of this is that for carrier-gradelinks, scintillation is not an issue and there-fore does not need to be addressed in the system design. System designs can include
features such as multiple laser transmitters to substantially reduce scintillation effects
for long links; however, as mentioned previously, this is not necessary on a carrier-
grade system since the link ranges are generally less than 500 m. Additionally, for car-
rier-grade systems, link margins are engineered to accommodate severe attenuation
conditions like fog, and therefore already have enough margin to take care of any scin-
tillation conditions since the air is always clear when it is highly scintillated.
Figure 19. Aperture-Averaging
0 1 2 30
1
2
3
43.338
0
prob I 100 m.,( )
prob I 1000 m.,( )
30.1 I
prob I R,( )
1
2 2 .. I.
R( ). A R( ).exp
ln I( ) 2
R( ) A R ( ).2
.
2
8
R( ) A R ( ).2
.
.
Aperture-averaging reduces
margin at distance
For a 75-mm aperture, the
increase in margin due to
scintillation for a
1 km link is about 13 dB when
aperture-averaging is taken into
account (fully saturated
atmosphere)
Scintillant size scales like
(R at =785 nm, R=1 km
(this is about 2.8 cm)
1/2
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The Physics of Free-Space Optics 21
Power Control and Eye Safety
Laser reliability is an issue for carrier-grade free-space optical systems that need to
have mean-time between failures (MTBF) of 8 years or more. There are basically two
factors that influence the lifetime of a semiconductor diode laserthe average operat-
ing temperature of the case of the diode, and the average operating output optical
power of the diode. For AlGaAs diode lasers, the activation energy is about 0.65 eV,
which implies that the lifetime of the diode increases by about a factor of two for every10C decrease in the average operating temperature of the diode case. The top graph of
figure 20 shows how the lifetime increases as a function of case temperature. For out-
door equipment a general rule of thumb for most locations in the world is that an aver-
age temperature of 2530C can be used to predict thermal effects on lifetime.
More important than thermal effects is the average output power of the laser. In this
case the lifetime scales inversely with the cube of the power, as illustrated in the bot-
tom graph of figure 20. This means that significant lifetime increases can be obtained
by systems that automatically control the output laser power since most of the time a
given link transmits through clear air and the output power can be reduced substan-
tially. Note that a distinction is made between automatic control of the output laser
power and attenuation of power using a filter, which does not provide the same laser
lifetime advantages. Systems that do not employ power control will probably have avery difficult time meeting carrier MTBF expectations.
Figure 20. Laser Reliability
Laser Life vs Output Power
(assumes constant temp)
0
20
40
60
80
100
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Average Laser Output Power (mW)
Y
ears
Laser Life vs Temp
(assumes constant power)
0
20
40
60
80
100
0 5 10 15 20 25 30 35 40 45
Avg Ext Ambient Temp (C)
Years
Laser lifetime approximately
doubles for every 10C decrease
in case temperature (activation
energy 0.65 eV)
Laser lifetime scales approxi-
mately as 1/P . For example,
a diode rated at 40 mW maximum
output power gets a lifetime
boost of 64x if run at 10 mW
3
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Eye safety is also a concern among large service providers. There are primarily two
classes of eye safety that free-space vendors build toClass 1 and Class 1M. Basically,
Class 1 certifies that the beam can be viewed under any condition without causing
damage to the eye. Class 1M certifies that the beam can be viewed under any condition
exceptby means of an aided viewing device, such as a binocular or other optical instru-
ment. In terms of wavelength, the IEC60825 rulings permit 1550 nm devices to output
about 50 times the flux level of near IR devices such as 780 nm lasers. While this can be
an advantage, the detectors at 1550 nm are noisier; therefore, on a system level,although there is a slight advantage for link margin, it is usually at a substantial
increase in cost, especially for carrier-grade systems where the atmosphere is the limit-
ing variable in the link equation as discussed previously. The subject of eye safety is
fairly arcane; for a good discussion see Eye Safety and Wireless Optical Networks
(WONs)by Jim Alwan, AirFiber Inc.
SUMMARY In summary, free-space optical systems can be enhanced to carrier-grade (99.9% or bet-ter) by following the simple design rules below, which apply for the vast majority of cit-
ies on the planet:
Atmospheric physics fundamentally limit range to less than 500 m. Accept and
design the hardware to meet this limit.
The equipment must be hardened to withstand the rigors of an outdoor environ-
ment. It mustmeet Telcordia GR-63, GR-487, and NEBS Level 3 product integrity
standards.
Carrier grade systems mustinclude tracking. This is the onlyway to guarantee link
margin.
Carrier grade systems musthave a carrier-class EMS.
Carrier grade systems mustmeet Class 1M or Class 1 laser eye-safety standards as
defined in IEC 60825 rulings.
Carrier grade systems should include an in-band management channel. This per-
mits the carrier to avoid building an overlay network to manage the free-space opti-
cal units.
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